in Magnetic Circuits. 



325 



joint will serve to show the relation of 33 to the externally 

 applied magnetic force on a ring with a joint if we re-draw it, 

 merely shearing it over by inclining the axis along which 33 

 is represented through an angle the tangent of which (inter- 

 preted upon the proper scale of 33 and of «£)) is equal to 



rn 



p To take a practical instance, suppose we have a ring of 



soft iron forming a magnetic circuit say 30 cm. long. Sup- 

 pose the ring, when tested in the solid state, to give the 

 curves of 33 and <£j shown in fig. 3, which are actual curves 



Fiar. 3. 



•1 , j I 1 



•"^-____- 



\ 10000 ^""""^ 



T^^ 



\ OOCJ0T // 



r 



1 V / ~ay 



_| ft >oo /A 





\ / // 



\ I 700 ° // 





\\ i 6000^ // 





A "5 // 



/\ 500 0^ // 



1 



! I \ 4000^ // 





I \3000N 1\ 





I f 1A000 / 1 





\ / 



! • io\oo / 



1 



1 j Mm- 





1 Maqncfr 



> 7 



1 



c Force 



| 



T 



1 



for a soft wrought-iron ring. Let it be required to deduce 

 from these curves the relation which the magnetism would 

 have to the externally applied magnetizing force if the ring, 

 instead of being solid, were cut into two half rings, with 

 carefully faced ends placed in the best possible contact. Each 

 cut, as we have seen, is equivalent to a gap 3 J^ cm. wide. 

 The two together make x equal to ¥B ^ of the length of the 

 ring. Hence, if we draw a line 0P(j in the figure inclined 

 so that £ is — 1 when 23 is 4500, the intercepts between it 

 Phil. Mag. S. 5. V 1. 34. No. 209. Oct. 1892. 2 A 



